Bill, the point about the examples of David, et al, is simply that they run counter to the presuppositions of certain credos (in this case, White). They must be considered, not simply dismissed. If we were dealing with logic, we would term these as counterexamples to show that the premise is false. Do they prove the paedo position outright? Of course not. But they do draw into question some of the assumptions that credos sometimes put forward.
With regard to Lydia and the Philippian jailer, the faith of their households (despite certain poor translations in the case of the jailer) is not mentioned, but must be assumed or inferred by the credobaptist. You are correct in that the continuity of the Abrahamic covenant is probably the strongest argument in favor of the paedo position. The point of mentioning the household baptisms in Acts is to show that this practice is consistent with with mode of the Abrahamic covenant, not a radical departure from it in terms of continuity.
Tim, you are exactly right about the household baptisms. They say MUCH more about the situation than credos want to admit to.
So, look at the example of Lydia. The text clearly states that the Lord opened HER heart to the things being spoken. It then states "and when she and her HOUSEHOLD were baptized." The text says nothing about the other members making a profession of faith; the credos assume this by inference because of their existing presuppositions.
But further in the passage, she says something interesting: "if you have judged ME to have been faithful, then come and stay at my house." Note carefully she does not say US, but rather ME.
This is very peculiar. Why would she emphasis only herself? Did not the professions of the other members of her household matter? What if Paul or Silas had said "well, Lydia, we have judged you to be faithful, but I'm not sure about the other members of your household." Wouldn't that have mattered? These are not inconsequential considerations.
The case of the jailer is very clear. In the greek, the participial phrase "having believed in God," is masculine singular, and refers to the jailer based on the grammatical context. In fact, I have even seen credo commentaries that interpret the passage "and his household rejoiced with him in that HE believed in God."
In his 1978 book "infant baptism and the covenant of grace," which promotes the credo position, Paul Jewitt readily admits this is what the text says. But being backed into a corner, Jewitt then says "well, how is it then that the household rejoiced? How could an infant do that?"
But one can easily refer to a household generically without necessarily referencing every single member of the household. One could refer to several members without including every single member and still say "household." This is commonly done in everyday language.
If I come home and announce to my family that I got a raise (I know, rare these days), they can REJOICE with me, while my infant may not know what is going on. The younger children rejoice because they see my wife and I rejoicing while not really understanding what a raise is. But the fact is I ALONE received the raise; I can tell others that my household rejoiced with me without meaning that the infant provided a rejoicing cackle as acknowledgement. So Dr. Jewitt's argument is simply a red herring.
Hope this is helpful.
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